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MoeBlee wrote:
> Rupert wrote:
> > That looks good to me. David's proof looks good to me as well.
>
> So would I be correct to take it that the consensus is that the theorem
> almost surely needs choice?
>
No, David's proof is correct and doesn't use choice.
> If that is the case, I find it interesting that this is not mentioned
> much (if at all) in basic textbooks. It seems so intuitive that for any
> set there is an equinumerous set disjoint from the original set, so the
> need for the axiom of choice would be another in the list of "reasons"
> for the axiom.
>
> MoeBlee
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